Unimodality, Log-concavity, Real-rootedness of independence polynomial of a graph

: 15h00, ngày 10/06/2022 (Thứ Sáu)

: P104 D3

: Seminar Toán rời rạc

: Đỗ Trọng Hoàng

: Viện Toán ứng dụng và Tin học, ĐH Bách Khoa Hà Nội

Tóm tắt báo cáo

A polynomial $P(x) = \sum_{k=0}^n a_kx^k$ with real coefficients is called:
\begin{itemize}
\item {\it unimodal} if there is $k$ such that $a_0\le \cdots \le a_{k-1}\le a_k \ge a_{k+1}\ge \cdots \ge a_n$.
\item \textit{log-concave} if the inequality $a_i^2\ge a_{i-1}a_{i+1}$ is valid for every $1\le i\le n-1$.
\item \textit{real-rooted} if all its zeros are real.
\end{itemize}
In this talk, we survey the important results referring the unimodality, log-concavity, and real-rootedness of independence polynomial of a graph. Some recent results in cooperation with colleagues will be also presented.


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